Periodic orbits of Linear and invariant flows on connected Lie groups
Abstract
Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is based on the eigenvalues of the derivation $\mathcal{D}$. From this, we study periodic orbits of a linear flow on noncompact, semisimple Lie groups, and we work with periodic orbits of a linear flow on connected, simply connected, solvable Lie groups of dimension 2 or 3.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.08479
 Bibcode:
 2020arXiv200208479S
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 13 pages